The motivation for this test is to show that the aggregated finite element method leads to a well-posed discrete system for which one can readily use standard iterative solvers and preconditioners. To this end, we consider the widely available linear solvers available in the PETSc library [1]}. We use a conjugate gradient method from the KSP module of PETSc, preconditioned with the smoothed-aggregation algebraic multigrid preconditioner GAMG [2]}. We set up the linear solver by relying as much as possible on the default configuration given by GAMG to effectively show that the aggregated finite element spaces lead to linear systems that can be efficiently solved using standard multigrid tools. The software used for these experiments is the MPI-parallel implementation of the AgFEM available at FEMPAR [3]} linked with p4est v2.0 [4]} for octree mesh handling and \(\mathtt {PETSc}\)  v3.9.0 [1]} for distributed-memory linear algebra data structures and solvers.
